(CNN) -- When Rabbi Jack Moline recently confronted his friend Rahm Emanuel about mounting Jewish anxiety over the Obama administration's Mideast policy, he was surprised at the White House Chief of Staff's response: to invite Moline and more than a dozen other rabbis to the White House for a nearly two-hour conversation.
But what really surprised Moline, who leads a northern Virginia synagogue, was that Emanuel invited the whole group back a couple of weeks ago for another long sit-down.
"We invited rabbis who'd been supportive of the president since the election," said Moline, who helped organize the two meetings of rabbis from across the country. "And who found themselves concerned about his approach to the Middle East process."
As the Obama administration steps up efforts to restart the Middle East peace process -- with U.S.-moderated talks between Israel and Palestinian leaders starting earlier this month and Israeli Prime Minister Benjamin Netanyahu scheduled to visit the White House next week -- it has launched a simultaneous campaign to allay fears within the American Jewish community over how that process will work.
Last week, President Barack Obama invited dozens of Jewish members of Congress to discuss his Mideast policy. On Thursday, Obama and his wife, Michelle, are hosting the first-ever White House event to honor Jewish Heritage Month. And White House officials have been meeting with other Jewish leaders on an ad hoc basis in recent weeks.
"With proximity talks restarted and some movement with respect to Iran and the U.N. Security Council, this is an important time to update folks on policy," said White House spokesman Tommy Vietor.
"Our policies haven't changed, we're just making sure we communicate them as clearly as possible," he said. "Some of that is outreach and some of that is in speeches we've seen by administration officials."
Many American Jewish leaders have expressed frustration at the Obama administration's public criticism of Israel and have questioned its approach to Iran, which the Jewish state views as a major security threat.
"There was an impression that the U.S. was singling out Israel for criticism," says Abraham Foxman, national director of the Anti-Defamation League, who recently met with White House aides, "while the Palestinians weren't being asked to do very much."
That sentiment boiled over in March, when Israel announced a plan to build 1,600 apartments in an area of Jerusalem claimed by both Israelis and Palestinians after the Obama administration had called for a halt to new Jewish West Bank settlements.
Vice President Joe Biden, who was visiting Israel at the time, denounced the move as "precisely the kind of step that undermines the trust we need right now." Secretary of State Hillary Clinton called the announcement "insulting" because it coincided with Biden's visit.
But some American Jewish leaders felt the administration's criticism went too far because, they argued, the housing project is in Jerusalem and not the West Bank.
Several weeks later, author and historian Elie Wiesel published ads in a handful of major American newspapers that seemed to criticize the Obama administration on Jerusalem.
"It is mentioned more than six hundred times in Scripture -- and not a single time in the Koran," the ad said of Israel's capital.
A few weeks after that, Obama hosted Wiesel for lunch at the White House.
Jewish leaders critical of the White House say their complaints extend beyond Jerusalem to the administration's general tone toward the Jewish state.
"One thing the rabbis emphasized is that we're not hearing and seeing enough from the president himself," said Moline, who is also director of public policy for the Rabbinical Assembly, the international association of Conservative rabbis.
"We would like him to make a trip to Israel," Moline said, "especially because he's been to the Middle East a couple times already and has not dropped in just to say hello."
The administration's early advocacy for attempting to engage Iran also upset many American Jewish groups, though the White House has stressed in meetings with Jewish leaders that it is pursing U.N. sanctions against the Islamic republic.
Some more progressive Jewish groups, meanwhile, are attempting to give Jewish cover to the administration's efforts to reignite the Mideast peace process.
"There's a lot of political gamesmanship happening right now," said Jeremy Ben-Ami, president of the dovish American Jewish group J Street, referring to Jewish leaders criticizing the White House. "The reality is that anyone who has followed this issue knows there's going to be a compromise on Jerusalem."
Next week, J Street is planning to launch a campaign called "The Community of Yes," to support the administration's Mideast policy in the face of what Ben-Ami says is a "chorus of no" from some Jewish leaders and groups.
An American Jewish Committee survey in March showed that 55 percent of American Jews approve of Obama's handling of U.S.-Israel relations.
Still, Jews are among the country's most Democratic constituencies, with nearly eight in 10 backing Obama in 2008.
Shmuley Boteach, a prominent American rabbi and commentator, predicts that support will slip in 2012.
"I cannot begin to convey the sense of outrage across the board in the Jewish community," over Obama's approach to the Middle East, he said.
Other Jewish leaders say they're withholding judgment on the administration's handling of the Mideast after receiving assurances of its support for Israel.
"These are cosmetic efforts," Foxman said of recent White House overtures. "The real question is about the content and impact of policy."